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arXiv · 2403.01574

On $\mathfrak{L}_{\infty}$-liftings of the Gelfand-Naimark morphism

Vasily Melnikov
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Abstract

Let $M$ be a $W^{\ast}$-algebra acting on a separable complex Hilbert space $H$. We show that the inclusion of $M$ into $\mathscr{B}(H)$ factors through an $\mathfrak{L}_{\infty}$-space only if $M$ is a finite type $\mathrm{I}$ algebra.

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Vasily Melnikov. 2024-03-03. On $\mathfrak{L}_{\infty}$-liftings of the Gelfand-Naimark morphism. https://doi.org/10.4213/mzm14258

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